2. a) The adjustable voltage source Vs is set at 12 V in the circuit below. Determine the nodalcomplexity of the circuit and, accordingly, solve for the current I under this condition.2000 Ix1 k22 k2Vs2 kn3 mA3 k2Vob) What is the value of Vo under this condition?c) The voltage source Vs is then adjusted until I, = 0 A. What would be the values of Vsand Vo under this new condition?

Answered: 2. a) The adjustable voltage source Vs…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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2. a) The adjustable voltage source Vs is set at 12 V in the circuit below. Determine the nodal
complexity of the circuit and, accordingly, solve for the current I under this condition.
2000 Ix
1 k2
2 k2
Vs
2 kn
3 mA
3 k2
Vo
b) What is the value of Vo under this condition?
c) The voltage source Vs is then adjusted until I, = 0 A. What would be the values of Vs
and Vo under this new condition?

Expert Solution

Step 1

For the given circuit, labeling the nodes across the dependent voltage source as shown in the figure below.

Step 2

Applying nodal analysis,

$I = \frac{V_{1} + V_{S}}{2 \times 10^{3}} + I_{x} 10^{3} I = 0.5 (V_{1} + V_{S}) + 10^{3} I_{x} . . . (1), I + 0.003 - \frac{V_{2}}{3 \times 10^{3}} = 0 10^{3} I = 0.333 V_{2} - 3 . . . (2), V_{2} - V_{1} = 2000 I_{x} . . . (3) .$

Step 3

Plugging the value $V_{s} = 12$ V,

$10^{3} I = 0.5 (V_{1} + 12) + 10^{3} I_{x} 10^{3} I = 0.5 V_{1} + 10^{3} I_{x} + 6 . . . (4) .$

Using equation (2) here,

$0.333 V_{2} - 3 = 0.5 V_{1} + 10^{3} I_{x} + 6 0.5 V_{1} - 0.333 V_{2} + 10^{3} I_{x} = - 9 . . . (5) .$

Applying Ohm's law,

$V_{1} = 2 \times 10^{3} I_{x} = 2000 I_{x} . . . (6) .$

Solving equation (3), (5) and (6),

$V_{1} = - 27 V, V_{2} = - 54 V, I_{x} = - 13.5 mA.$

Answer (a): $I_{x} = - 13.5 mA .$

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